作 者：
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机构地区：
浙江万里学院计算机与信息学院
出 处：
《中国科学：数学》
2012年第7期699-709,共11页
摘 要：
对于Rn中满足0
Abstract For compact set K ∈R^n with 0 〈 H^8 （K） 〈 ∞ and any conformal bijection f, we obtain the Hausdorffmeasure of the conformal imageH^s（f（K））=H^s（K）·∫_K｜Dxf｜^s dμ（x）, whereμ=H^s｜K/H^s（K）is a probability measure. In particular, for any given self-similar set K satisfying the open set condition, the measure μ= is the corresponding self-similar measure, and thus we can calculate Hausdorff measure of f（K） by using the above formula. For example, K is the A-Sierpinski carpet with λ≤ 1/4 and f（z） = z ＋ εz^2 with ε ∈ C and ｜ε｜ ≤0.1 In this example, the image f（K） is a self-conformal set. Therefore, our algorithm can calculate the Hausdorff measures of a special class of self-conformal sets with nonlinear structure.
关 键 词：
测度
共形映射
自共形集
领 域：
[理学]
[理学]
